The paper represents a study on the characteristics and biocompatibility of tissue-engineering structures with nanocarbon scaffolds in the bioorganic matter for various bioengineering applications, including biomedical devices for the heart treatment and neurostimulation. These structures were obtained via a laser formation method. Structures were printed using previously developed laser setup and had a cellular structure in accordance to the cell monolayer formation. It was established that SWCNT bind to amino acids through oxygen atoms. It was observed that the SWCNT diameter increased due to their wrapping by a bioorganic matter. Moreover, electrical conductivity values of such structures exceeded the heart tissue conductivity (0.1 S/m) and reached 8.5 S/m. The proliferation of fibroblasts and endothelial cells on the studied structures was demonstrated via the fluorescence microscopy and the MTT assay. The density of proliferated cells on structures was higher than in control samples. Finally, the biodegradation rate of tissue-engineered structures during the implantation to laboratory animals was 75-90 days, the samples promoted neovascularization of the affected tissue.